Joined eyelids to mesh, but they remain stationary when animating
When you add some vertices to an already skinned mesh, the added vertices have no weight relatively to any bone, so you have to weight them manually (or do a new automatic weighting): the eyelids are supposed to move with the head bone.

To do so, select all the vertices of the  eyelids, go to vertex group tab in the properties panel, select the head vertex group and click assign.

If the eyelids doesn't move exactly with the other head vertices, check how the vertices near the eyelids are weighted in the "N" properties panel and weight the new vertices accordingly.

For a more complex rig you could add some new eyelids bones, parent them to the head bone, and assign eyelid vertices to them, in order to animate the eyelids. In this case you'll have to create some new vertex groups exactely named as the new bones and repeat the procedure above.